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arXiv 2203.11403hep-thgr-qc
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膜世界中由广义不确定性原理(GUP)给出的精细结构常数的量子引力约束

Quantum Gravity Constraints on Fine Structure Constant from GUP in Braneworlds

A. S. Lemos, F. A. Brito

AI总结:

本研究在厚膜世界框架下结合广义不确定性原理(GUP),分析时空几何对电磁作用的影响,推导高维时空下精细结构常数的修正,并通过实验数据约束相关量子引力参数,给出量子引力效应显现的中间长度标度。

摘要:

广义不确定性原理(Generalized Uncertainty Principle,GUP)已在厚膜世界场景中得到探讨。通过研究该背景下的里德伯原子,我们发现时空几何会影响麦克斯韦方程组,在空间中诱导出有效介电常数。相应地,经引力相互作用修正的库仑势会使三维玻尔半径产生偏差。随后,我们计算了高维时空中由GUP导致的精细结构常数修正。我们还通过将预测的偏差与最新的精细结构常数实验数据进行对比,得到了形变参数β和D维普朗克长度l_D的约束范围。我们计算了中间长度标度,原则上该标度可能大于普朗克长度标度。据推测,在该标度以下量子引力效应应当会显现。

英文摘要:

The Generalized Uncertainty Principle (GUP) has been discussed in the thick braneworld scenario. By considering Rydberg atoms in this background, we show that the spacetime geometry affects Maxwell equations inducing an effective dielectric constant on the space. In its turn, the corrected Coulomb potential by the gravitational interaction yields a deviation on the $3$-dimensional Bohr radius. Then, we compute the corrections on the fine structure constant owing to the GUP in higher-dimensional spacetime. We also found constraints for the deformation parameter $β$ and $D$-dimensional Planck length $l_{D}$ by comparing the predicted deviations with the recent empirical data of the fine structure constant. We compute the intermediate length scale, which in principle may be larger than the Planck length scale. It is conjectured that below such scale Quantum Gravity effects should take place.

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